We study heat conduction in a system of hard disks confined to a narrow two-dimensional channel. The
system is initially in a high-density solidlike phase. We study, through nonequilibrium molecular dynamics
simulations, the dependence of the heat current on an externally applied elongational strain. The strain leads to
deformation and failure of the solid and we find that the changes in internal structure can lead to very sharp
changes in the heat current. A simple free-volume-type calculation of the heat current in a finite hard-disk
system is proposed. This reproduces some qualitative features of the current-strain graph for small strains